Question

in a trial of 150 patients who received 10-mg doses of a drug daily, 36 reported headache as a side effect. use this information to complete parts (a) through (d) below. (a) obtain a point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect. (b) Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence satisfied? (a). Yes, they are satisfied (b). no, the requirement that each trial be dependent is not satisfied (c). no, the requirement that the sample size is no more than 5% of the population is not satisfied. (d) no, the requirement that np(1-p) is greater than 10 is not satisfied. (C) Construct a 99% confidence interval for the population proportion of patients who receive the drug and report headache as an effect. The 99% confidence interval is(___ , ___). (d) Interpret the confidence interval. Which statement below best interprets the interval? (a). There is 99% chance that the true value of p will not fall in the interval. (b). There is a 99% chance that the true value of p will fall in the interval. (c). We are 99% confident that the interval does not contain the true value of p. (d). We are 99% confident that the interval contains the true value of p.

Answer 1

A)

P (point estimate) = 36/150 = 0.24

B)

We need to check two conditions of normality,

N*p and n*(1-p) both are greater than 5 or not

N = 150

P = 0.24

N*p = 36 > 5

N*(1-p) = 114>5

Conditions are met.

C)

As the conditions of normality are met, we can use standard normal z table to estimate the confidence interval

From z table, critical value z for 99% confidence level is 2.58

Margin of error = z*√p*(1-p)/√n

P = 0.24

N = 150

Z = 2.58

MOE = 0.0899676741946

Confidence interval is given by

(P-MOE) < P < (P+MOE)

(0.1500323258053, 0.3299676741946)

D)

We are 99% confident that true value of p will lie in the interval.